A car sells for $\$5000$ and loses $\dfrac{1}{10}$ of its value each year. Write a function that gives the car's value, $V(t)$, $t$ years after it is sold. $V(t)=$
Solution: If the car loses $\dfrac{1}{10}$ of its value each year, that means $\dfrac{9}{10}$ of the value remains each year. So each year, the car's value is multiplied by a factor of $\dfrac{9}{10}$ (or $0.9$ ). If we start with the initial value, $\$5000$, and keep multiplying by $\dfrac{9}{10}$, this function gives us the car's value $t$ years from now: $V(t)=5000\left(\dfrac{9}{10}\right)^t$